Question

The sum of 'r' terms of an AP is $2r^2+3r$. Then, the $n^{th}$​ term is :

• A. 2n - 1
• B. 4n + 1
• C. 3n - 1
• D. 3n + 1

Answer 1

The correct option is B

4n + 1

$S_r=(2r^2+3r)$
$T_n=S_n-S_{n-1}$
So, $S_n=2n^2+3n$
$S_{n-1}=2{(n-1)}^2+3(n-1)$
Now,
$T_n=S_n-S_{n-1}$
$=2n^2+3n-\left[2\right(n^2-2n+1)+3n-3]$
$=2n^2+3n-2n^2+4n-2-3n+3=4n+1$